Form over Function Teaching Beginners How to Construct Programs - - PowerPoint PPT Presentation

Form over Function

Teaching Beginners How to Construct Programs Michael Sperber Collaborators: Marcus Crestani, Martin Gasbichler, Herbert Klaeren, Eric Knauel @ University of Tübingen

Back at the Ranch ...

Volker Claus’s Trick

So How Is This About Scheme?

? U

Self-Deception

• plagiarism
• stronger students are more vocal
• strong students teach themselves

• Syntax
• Size
• Functional
• Easy to transition to X

Scheme Is Great For Beginners

• Syntax
• Size
• Functional
• Easy to transition to X

Scheme Is Great For Beginners

Wrong Questions!

What Is Important to You?

Geometric Shapes

A geometric shape is one of the following:

• square (parallel to axes)
• circle
• overlay of 2 geometric shapes

Geometric Shapes

Implement geometric shapes! Write a program that allows creating geometric shapes und to check whether a given point is inside our outside a geometric shape!

Geometric Shapes

Shape Square Circle Overlay

Design Recipes

Page from English 6

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Data Analysis

• shapes
• squares
• circles
• overlays
• points
• (2-dimensional plane)

Mixed Data

A geometric shape is one of the following:

• a circle
• a square
• an overlay

Composite Data

A circle has:

• center
• radius

Design Recipe

“When your data analysis contains composite data, identify the signatures of the

• components. Then write a data definition

starting with the following:

; An x consists of / has: ; - field1 (sig1) ; ... ; - fieldn (sign)

Design Recipe

Then translate the data definition into a record definition:

(define-record-procedures sig constr pred? (select1 ... selectn)

Design Recipe

Also write a constructor signature of the following form:

(: constr (sig1 ... sign -> sig))

Also, write signatures for the predicate and the selectors:

(: pred? (any -> boolean)) (: select1 (sig -> sig1)) ... (: selectn (sig -> sign))

Circles

; A circle consists of: ; - center (point) ; - radius (real) (define-record-procedures circle make-circle circle? (circle-center circle-radius)) (: make-circle (point real -> circle)) (: circle? (any -> boolean)) (: circle-center (circle -> point)) (: circle-radius (circle -> real))

Composite Data

A square consists of:

• lower left corner
• size

Squares

; A square consists of: ; - lower left corner (point) ; - size / edge length (real) (define-record-procedures square make-square square? (square-corner square-size)) (: make-square (point real -> square)) (: square? (any -> boolean)) (: square-corner (square -> point)) (: square-size (square -> real))

Composite Data with Self Reference

On overlay consists of:

• a geometric shape
• and another geometric shape

Overlays

; An overlay consists of: ; - a geometric shape “on top” (shape) ; - a geometric shape “on bottom” (shape) (define-record-procedures overlay make-overlay overlay? (overlay-top-shape overlay-bot-shape)) (: make-overlay (shape shape -> overlay)) (: overlay? (any -> boolean)) (: overlay-top-shape (overlay -> shape)) (: overlay-bot-shape (overlay -> shape))

Points

; A point consists of: ; - x coordinate (real) ; - y coordinate (real) (define-record-procedures point make-point point? (point-x point-y)) (: make-point (real real -> point)) (: point? (any -> boolean)) (: point-x (point -> real)) (: point-y (point -> real))

Geometric Shapes

; A geometric shape is one of the following: ; - a circle (circle) ; - a square parallel to the axes (square) ; - on overlay of two geometric figures (overlay) (define shape (signature (mixed circle square

• verlay)))

Examples

Examples

(define p1 (make-point 10 20)) ; Point at X=10, Y=20 (define p2 (make-point 30 50)) ; Point at X=30, Y=50 (define p3 (make-point 40 30)) ; Point at X=40, Y=30 (define s1 (make-square p1 40)) ; Square w/ corner at p1, size 40 (define c1 (make-circle p2 20)) ; Circle around p2, radius 20 (define o1 (make-overlay c1 s1)) ; Overlay of circle und square (define c2 (make-circle p3 15)) ; Circle around p3, radius 10 (define o2 (make-overlay o1 c2)) ; Overlay of o1 and c2

First Steps

; is a point within a shape? (: point-in-shape? (point shape -> boolean)) (check-expect (point-in-shape? p2 c1) #t) (check-expect (point-in-shape? p3 c2) #t) (check-expect (point-in-shape? (make-point 51 50) c1) #f) (check-expect (point-in-shape? (make-point 11 21) s1) #t) (check-expect (point-in-shape? (make-point 49 59) s1) #t) (check-expect (point-in-shape? (make-point 9 21) s1) #f) (check-expect (point-in-shape? (make-point 11 19) s1) #f) (check-expect (point-in-shape? (make-point 51 59) s1) #f) (check-expect (point-in-shape? (make-point 49 61) s1) #f) (check-expect (point-in-shape? (make-point 40 30) o2) #t) (check-expect (point-in-shape? (make-point 0 0) o2) #f)

short description signature examples

Template

(define point-in-shape? (lambda (p s) ...))

Skeleton

(define point-in-shape? (lambda (p s) ... p ... s ... ... (point-x p) ... (point-y p) ... (cond ((circle? s) ...) ((square? s) ...) ((overlay? s) ...))))

More Skeleton

(define point-in-shape? (lambda (p s) ... p ... s ... ... (point-x p) ... (point-y p) ... (cond ((circle? s) ... (circle-center s) ... (circle-radius s) ...) ((square? s) ... (square-corner s) ... (square-size s) ...) ((overlay? s) ... (overlay-top-shape s) ... (overlay-bot-shape s) ...))))

More Skeleton

(define point-in-shape? (lambda (p s) ... p ... s ... ... (point-x p) ... (point-y p) ... (cond ((circle? s) ... (circle-center s) ... (circle-radius s) ...) ((square? s) ... (square-corner s) ... (square-size s) ...) ((overlay? s) ... (point-in-shape? p (overlay-top-shape s)) ... (point-in-shape? p (overlay-bot-shape s)) ...))))

Definition

(define point-in-shape? (lambda (p s) (cond ((circle? s) (<= (distance p (circle-center s)) (circle-radius s))) ((square? s) (and (>= (point-x p) (point-x (square-corner s))) (<= (point-x p) (+ (point-x (square-corner s)) (square-size s))) (>= (point-y p) (point-y (square-corner s))) (<= (point-y p) (+ (point-y (square-corner s)) (square-size s))))) ((overlay? s) (or (point-in-shape? p (overlay-top-shape s))

Refinement

(define point-in-shape? (lambda (p s) (cond ((circle? s) (<= (distance p (circle-center s)) (circle-radius s))) ((square? s) (let ((corner (square-corner s))) (let ((cx (point-x corner)) (cy (point-y corner)) (size (square-size s)) (x (point-x p)) (y (point-y p))) (and (>= x cx) (<= x (+ cx size)) (>= y cy) (<= y (+ cy size)))))) ((overlay? s) (or (point-in-shape? p (overlay-top-shape s)) (point-in-shape? p (overlay-bot-shape s)))))))

Enforcement

Enforcement

Enforcement

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Measure

Observe & Measure

Form

How Many Forms?

How Many Forms?

Scheme

... is our business!

Practice

So Why Again Is Scheme Important?

Signature violations

Properties

(check-property (for-all ((a number) (b number)) (= (+ a b) (+ b a))))

Properties

(: commutativity ((%a %a -> %b) signature -> property)) (define commutativity (lambda (op sig) (for-all ((a sig) (b sig)) (expect (op a b) (op b a)))))

Images

Why Not Start With Types?

data Tool1 = ... data ToolState1 = ... data Tool2 = ... data ToolState2 = ... data Tool = Tool1 | Tool2 data ToolState = ToolState1 | ToolState2

Summary

• Don’t love Scheme.
• Your students don’t have to love you.
• Only program what you can explain.
• Observe & measure.
• Kill your darlings.
• Fall in love with Scheme all over.

Collaboration Record